Problem: A big football championship will occur soon! n teams will compete in it, and each pair of teams will play exactly one game against each other.

There are two possible outcomes of a game:

  * the game may result in a tie, then both teams get 1 point; 
  * one team might win in a game, then the winning team gets 3 points and the losing team gets 0 points. 



The score of a team is the number of points it gained during all games that it played.

You are interested in a hypothetical situation when all teams get the same score at the end of the championship. A simple example of that situation is when all games result in ties, but you want to minimize the number of ties as well.

Your task is to describe a situation (choose the result of each game) so that all teams get the same score, and the number of ties is the minimum possible.

Input

The first line contains one integer t (1 ≤ t ≤ 100) — the number of test cases.

Then the test cases follow. Each test case is described by one line containing one integer n (2 ≤ n ≤ 100) — the number of teams.

Output

For each test case, print (n(n - 1))/(2) integers describing the results of the games in the following order: the first integer should correspond to the match between team 1 and team 2, the second — between team 1 and team 3, then 1 and 4, ..., 1 and n, 2 and 3, 2 and 4, ..., 2 and n, and so on, until the game between the team n - 1 and the team n.

The integer corresponding to the game between the team x and the team y should be 1 if x wins, -1 if y wins, or 0 if the game results in a tie.

All teams should get the same score, and the number of ties should be the minimum possible. If there are multiple optimal answers, print any of them. It can be shown that there always exists a way to make all teams have the same score.

Example

Input


2
2
3


Output


0 
1 -1 1 

Note

In the first test case of the example, both teams get 1 point since the game between them is a tie.

In the second test case of the example, team 1 defeats team 2 (team 1 gets 3 points), team 1 loses to team 3 (team 3 gets 3 points), and team 2 wins against team 3 (team 2 gets 3 points).

Solution (in JAVA):

Solution:

import java.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.util.*;


public class basecode {
    static final int MAXN = 1000_006;
    static final long MOD = (long) 1e9 + 7;
	public static void main(String[] args) throws IOException {
		MyScanner s = new MyScanner();
		Print p = new Print();
		int t = s.nextInt();
		
		while (t-- > 0) {
			int n = s.nextInt();
			if (n % 2 == 1) {
				for (int i = 0; i < n; i++) {
					for (int j = i + 1; j < n; j++) {
						if (j - i <= n / 2) {
							p.print(1 + " ");
						} else {
							p.print(-1 + " ");
						}
					}
				}
				p.println("");
			} else {
				for (int i = 0; i < n; i++) {
					for (int j = i + 1; j < n; j++) {
						if (j - i < n / 2) {
							p.print(1 + " ");
						} else if (j - i == n / 2) {
							p.print(0 + " ");
						} else {
							p.print(-1 + " ");
						}
					}
				}
				p.println("");
			}
		}
		p.close();
	}
	
	public static class Pair implements Comparable<Pair> {
		
		int first;
		
		int second;
		
		public Pair(int a, int b) {
			this.first = a;
			this.second = b;
		}
		
		@Override
		public int hashCode() {
			final int prime = 31;
			int result = 1;
			result = prime * result + first;
			result = prime * result + second;
			return result;
		}
		
		@Override
		public boolean equals(Object obj) {
			if (this == obj)
				return true;
			if (obj == null)
				return false;
			if (getClass() != obj.getClass())
				return false;
			Pair other = (Pair) obj;
			if (first != other.first)
				return false;
			if (second != other.second)
				return false;
			return true;
		}
		
		@Override
		public int compareTo(Pair o) {
			// TODO Auto-generated method stub
			return o.first - first;
		}
		
	}
	
	public static class Helper {
	    long MOD = (long) 1e9 + 7;
	    int MAXN = 1000_006;;
	    Random rnd;
	 
	    public Helper(long mod, int maxn) {
	        MOD = mod;
	        MAXN = maxn;
	        rnd = new Random();
	    }
	    
	    public Helper() {
	    	
	    }
	    
	    public static int[] sieve;
	    public static ArrayList<Integer> primes;
	 
	    public void setSieve() {
	        primes = new ArrayList<>();
	        sieve = new int[MAXN];
	        int i, j;
	        for (i = 2; i < MAXN; ++i)
	            if (sieve[i] == 0) {
	                primes.add(i);
	                for (j = i; j < MAXN; j += i) {
	                    sieve[j] = i;
	                }
	            }
	    }
	 
	 
	    public static long[] factorial;
	 
	    public void setFactorial() {
	        factorial = new long[MAXN];
	        factorial[0] = 1;
	        for (int i = 1; i < MAXN; ++i) factorial[i] = factorial[i - 1] * i % MOD;
	    }
	 
	    public long getFactorial(int n) {
	        if (factorial == null) setFactorial();
	        return factorial[n];
	    }
	 
	    public long ncr(int n, int r) {
	        if (r > n) return 0;
	        if (factorial == null) setFactorial();
	        long numerator = factorial[n];
	        long denominator = factorial[r] * factorial[n - r] % MOD;
	        return numerator * pow(denominator, MOD - 2, MOD) % MOD;
	    }
	 
	 
	    public long[] getLongArray(int size, MyScanner s) throws Exception {
	        long[] ar = new long[size];
	        for (int i = 0; i < size; ++i) ar[i] = s.nextLong();
	        return ar;
	    }
	 
	    public int[] getIntArray(int size, MyScanner s) throws Exception {
	        int[] ar = new int[size];
	        for (int i = 0; i < size; ++i) ar[i] = s.nextInt();
	        return ar;
		}
	 
	    public int[] getIntArray(String s)throws Exception
	    {
	        s = s.trim().replaceAll("\\s+", " ");
	        String[] strs = s.split(" ");
	        int[] arr = new int[strs.length];
	        for(int i = 0; i < strs.length; i++)
	        {
	            arr[i] =  Integer.parseInt(strs[i]);
	        }
	        return arr;
	    }
	 
		public long gcd(long a, long b) {
	        return b == 0 ? a : gcd(b, a % b);
	    }
	 
	    public int gcd(int a, int b) {
	        return b == 0 ? a : gcd(b, a % b);
	    }
	 
	 
	    public long max(long[] ar) {
	        long ret = ar[0];
	        for (long itr : ar) ret = Math.max(ret, itr);
	        return ret;
	    }
	 
	    public int max(int[] ar) {
	        int ret = ar[0];
	        for (int itr : ar) ret = Math.max(ret, itr);
	        return ret;
	    }
	 
	    public long min(long[] ar) {
	        long ret = ar[0];
	        for (long itr : ar) ret = Math.min(ret, itr);
	        return ret;
	    }
	 
	    public int min(int[] ar) {
	        int ret = ar[0];
	        for (int itr : ar) ret = Math.min(ret, itr);
	        return ret;
	    }
	 
	 
	    public long sum(long[] ar) {
	        long sum = 0;
	        for (long itr : ar) sum += itr;
	        return sum;
	    }
	 
	    public long sum(int[] ar) {
	        long sum = 0;
	        for (int itr : ar) sum += itr;
	        return sum;
	    }
	 

	 
	    public long pow(long base, long exp, long MOD) {
	        base %= MOD;
	        long ret = 1;
	        while (exp > 0) {
	            if ((exp & 1) == 1) ret = ret * base % MOD;
	            base = base * base % MOD;
	            exp >>= 1;
	        }
	        return ret;
	    }
	 

	}

	
    static class Print {
        private BufferedWriter bw;
 
        public Print() {
            this.bw = new BufferedWriter(new OutputStreamWriter(System.out));
        }
        public void print(Object object) throws IOException {
            bw.append("" + object);
        }
        public void println(Object object) throws IOException {
            print(object);
            bw.append("\n");
        }
        public void close() throws IOException {
            bw.close();
        }
    }
	
	
	
	
	
	
    public static class MyScanner {
	      BufferedReader br;
	      StringTokenizer st;
	 
	      public MyScanner() {
	         br = new BufferedReader(new InputStreamReader(System.in));
	      }
	 
	      String next() {
	          while (st == null || !st.hasMoreElements()) {
	              try {
	                  st = new StringTokenizer(br.readLine());
	              } catch (IOException e) {
	                  e.printStackTrace();
	              }
	          }
	          return st.nextToken();
	      }
	 
	      int nextInt() {
	          return Integer.parseInt(next());
	      }
	 
	      long nextLong() {
	          return Long.parseLong(next());
	      }
	 
	      double nextDouble() {
	          return Double.parseDouble(next());
	      }
	 
	      String nextLine(){
	          String str = "";
		  try {
		     str = br.readLine();
		  } catch (IOException e) {
		     e.printStackTrace();
		  }
		  return str;
	      }
	}


}